Related papers: A numerical ampleness criterion via Gale duality

We prove a Kodaira-type vanishing theorem for the Witt vector sheaf on a Fano variety over a perfect field of characteristic p. As a corollary, we deduce that the number of rational points on a Fano variety over a finite field with q=p^n…

Topological invariants such as characteristic classes are an important tool to aid in understanding and categorizing the structure and properties of algebraic varieties. In this note we consider the problem of computing a particular…

Any ample Cartier divisor D on a projective variety X is strictly nef (i.e. D.C>0 for any effective curve C on X). In general, the converse statement does not hold. But this is conjectured to be true for anticanonical divisors. The present…

We associate to each toric vector bundle on a toric variety X(Delta) a "branched cover" of the fan Delta together with a piecewise-linear function on the branched cover. This construction generalizes the usual correspondence between toric…

We give a necessary and sufficient condition for the integrality of the Taylor coefficients at the origin of formal power series $q_i({\mathbf z})=z_i\exp(G_i({\mathbf z})/F({\mathbf z}))$, with ${\mathbf z}=(z_1,...,z_d)$ and where…

Let X be a toric variety over a number field k with \kbar[X]^\times=\kbar^\times. Let W\subset X be a closed subset of codimension at least 2. We prove that X\setminus W satisfies strong approximation with algebraic Brauer--Manin…

In this article we consider structures on a Fano plane ${\cal F}$ which allow a generalisation of Freudenthal's construction of a norm and a bilinear multiplication law on an eight-dimensional vector space ${\mathbb O_{\cal F}}$ canonically…

Let $p$ be a prime, and $N$ be a positive integer not divisible by $p$. Denote by ${\rm ord}_N(p)$ the multiplicative order of $p$ modulo $N$. Let $\mathbb{F}_q$ represent the finite field of order $q=p^{{\rm ord}_N(p)}$. For $a,…

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary…

Let $K/\mathbb{Q}$ be an algebraic extension of fields, and let $\alpha \not= 0$ be contained in an algebraic closure of $K$. If $\alpha$ can be approximated by roots of numbers in $K^{\times}$ with respect to the Weil height, we prove that…

Let $X$ be a $\mathbb Q$-Fano variety admitting a K\"ahler-Einstein metric. We prove that up to a finite quasi-\'etale cover, $X$ splits isometrically as a product of K\"ahler-Einstein $\mathbb Q$-Fano varieties whose tangent sheaf is…

Given a Weil non-integral divisor $D$, it is natural to associate it the line bundle of its integral part $\mathcal{O}_X([D])$. In this work we study which of the classical characterizations of ample and big divisors can be extended to…

We show that being a general fibre of a Mori fibre space is a rather restrictive condition for a Fano variety. More specifically, we obtain two criteria (one sufficient and one necessary) for a Q-factorial Fano variety with terminal…

We define a Weil-\'etale complex with compact support for duals (in the sense of the Bloch dualizing cycles complex $\mathbb{Z}^c$) of a large class of $\mathbb{Z}$-constructible sheaves on an integral $1$-dimensional proper arithmetic…

Given a variety defined over a field of characteristic zero and an algebraically integrable foliation of corank less than or equal to two, we show the existence of a categorical quotient, defined on the non-empty open set of stable points,…

For $\epsilon$-lc Fano type varieties $X$ of dimension $d$ and a given finite set $\Gamma$, we show that there exists a positive integer $m_0$ which only depends on $\epsilon,d$ and $\Gamma$, such that both $|-mK_X-\sum_i\lceil mb_i\rceil…

The Weil restriction functor, introduced in the late fifties, was recently extended by Karpenko to the category of Chow motives with integral coefficients. In this article we introduce the noncommutative (=NC) analogue of the Weil…

Given an $n$-ary $k-$valued function $f$, $gap(f)$ denotes the minimal number of essential variables in $f$ which become fictive when identifying any two distinct essential variables in $f$. We particularly solve a problem concerning the…

In the Laguerre ensemble of N x N (positive) hermitian matrices, it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic, denoted var_N f, as N->infinity.…

Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of functions which are "fractionally computable" by a partial…